This is correct.
The first paper to describe a stepwise model was by Royce in 1970 [1]. The model he is describing is hypothetical and does not use the term Waterfall.
The first use of the word "waterfall" (including the quotation marks) is from 1976 [2] and specifically refers to [1], the hypothetical model. In [2], the writers specifically state that "so few" projects fit this scheme.
If you were programming in the 80s and early 90s, you would know that no one in programming ever referred to a "waterfall" model.
Even Kent Beck's seminal book on XP, written in 2000, describes many failures of software development in those days, but he does not once use the word Waterfall.
So, in summary: the paper that supposedly describes it describes a hypothetical system; the paper that first uses the term mentions how little the model is used; the term wasn't used by people during the era it was supposedly most popular; and the folks who initiated the new generation of software dev don't refer to the model.
I think it's safe to say that it was not a thing. Or, to be more accurate, if it was a thing, it was never the thing it became until the Agile consultants used is as a strawman.
[1] http://www.cs.umd.edu/class/spring2003/cmsc838p/Process/wate...